# Neural KEM: A Kernel Method with Deep Coefficient Prior for PET Image Reconstruction

arXiv: https://arxiv.org/abs/2201.01443 · HTML: https://mlsanity.com/paper/2201.01443/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 49 references that are in the map.
- First posted on arXiv 5 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Iterative PET Image Reconstruction Using Convolutional Neural Network Representation](https://mlsanity.com/paper/1710.03344/) (2017)
- [Direct Reconstruction of Linear Parametric Images from Dynamic PET Using Nonlocal Deep Image Prior](https://mlsanity.com/paper/2106.10359/) (2021)
- [Deep Kernel Representation for Image Reconstruction in PET](https://mlsanity.com/paper/2110.01174/) (2021)
- [Penalized-likelihood PET Image Reconstruction Using 3D Structural Convolutional Sparse Coding](https://mlsanity.com/paper/1912.07180/) (2019)

## Built on by (most cited first, 5 of 5)

- [DULDA: Dual-domain Unsupervised Learned Descent Algorithm for PET image reconstruction](https://mlsanity.com/paper/2303.04661/) (2023)
- [List-Mode PET Image Reconstruction Using Dykstra-Like Splitting](https://mlsanity.com/paper/2403.00394/) (2024)
- [Deep kernel representations of latent space features for low-dose PET-MR imaging robust to variable dose reduction](https://mlsanity.com/paper/2409.06198/) (2024)
- [Physics-Constrained Diffusion Reconstruction with Posterior Correction for Quantitative and Fast PET Imaging](https://mlsanity.com/paper/2508.14364/) (2025)
- [A Kernel Space-based Multidimensional Sparse Model for Dynamic PET Image Denoising](https://mlsanity.com/paper/2509.18801/) (2025)

## Abstract (arXiv)

Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The kernelized expectation-maximization (KEM) algorithm has been developed and demonstrated to be effective and easy to implement. A common approach for a further improvement of the kernel method would be adding an explicit regularization, which however leads to a complex optimization problem. In this paper, we propose an implicit regularization for the kernel method by using a deep coefficient prior, which represents the kernel coefficient image in the PET forward model using a convolutional neural-network. To solve the maximum-likelihood neural network-based reconstruction problem, we apply the principle of optimization transfer to derive a neural KEM algorithm. Each iteration of the algorithm consists of two separate steps: a KEM step for image update from the projection data and a deep-learning step in the image domain for updating the kernel coefficient image using the neural network. This optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations and real patient data have demonstrated that the neural KEM can outperform existing KEM and deep image prior methods.